On the geometric structure of spatio-temporal patterns

Erhardt Barth and Mario Ferraro&

Institute for Signal Processing
Medical University of Luebeck
Ratzeburger Allee 160, 23538 Luebeck, Germany
& Dipartimento di Fisica Sperimentale and INFM
via Giuria 1, Torino



The structure of hypersurfaces corresponding to different spatio-temporal patterns is considered, and in particular representations based on geometrical invariants, such as the Riemann and Einstein tensors and the scalar curvature are analyzed. The spatio-temporal patterns result from translations, Lie-group transformations, accelerated and discontinuous motions and modulations. Novel methods are obtained for the computation of motion parameters and the optical flow. Moreover, results obtained for accelerated and discontinuous motions are useful for the detection of motion boundaries.
Full paper in PDF format

The formulas that were too large to be printed in the paper can be downloaded here:

  Related applications have been presented in
Bewegung als intrinsische Geometrie von Bildfolgen and
Spatio-temporal curvature and the visual coding of motion